The reaction yield for conversion of p-nitrobenzaldehyde (PNB) to an aldol product in amine-functionalized mesoporous silica nanoparticles (MSN) exhibits a 20-fold enhancement for a modest increase in pore diameter, d. This enhanced catalytic activity is shown to reflect a strong increase in the “passing propensity,” $\mathcal{P}$, of reactant and product species inside the pores. We find that $\mathcal{P}$ ≈ 0, corresponding to single-file diffusion, applies for the smallest d which still significantly exceeds the linear dimensions of PNB and the aldol product. However, in this regime of narrow pores, these elongated species must align with each other and with the pore axis in order to pass. Thus, $\mathcal{P}$ reflects both translational and rotational diffusion. Langevin simulation accounting for these features is used to determine $\mathcal{P}$ versus d. The results are also augmented by analytic theory for small and large d where simulation is inefficient. The connection with the catalytic activity and yield is achieved by the incorporation of results for $\mathcal{P}$ into a multi-scale modeling framework. Specifically, we apply a spatially coarse-grained (CG) stochastic model for the overall catalytic reaction-diffusion process in MSN. Pores are treated as linear arrays of cells from the ends of which species adsorb and desorb, and between which species hop and exchange, with the exchange rate reflecting $\mathcal{P}$. CG model predictions including yield are assessed by Kinetic Monte Carlo simulation.

中文翻译：

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孔径与催化活性的关系：在胺官能化的介孔二氧化硅中，对硝基苯甲醛转化为醛醇产物

在胺官能化的介孔二氧化硅纳米颗粒（MSN）中，对硝基苯甲醛（PNB）转化为醛醇产物的反应收率显示出20倍的增加，孔径d适度增加。研究表明，这种增强的催化活性反映出“通过倾向”的大幅增加，$\mathcal{P}$孔中的反应物和产物种类。我们发现$\mathcal{P}$对应于单文件扩散的≈0适用于仍明显超过PNB和羟醛产物的线性尺寸的最小d。但是，在这种狭窄的孔隙状态下，这些伸长的物种必须彼此对齐并且与孔隙轴对齐才能通过。因此，$\mathcal{P}$反映了平移和旋转扩散。考虑这些功能的Langevin仿真用于确定$\mathcal{P}$与d。对于模拟效率不高的小和大d的分析理论，结果也得到了增强。与催化活性和产率的联系是通过结合以下结果实现的$\mathcal{P}$成为一个多尺度的建模框架。具体来说，我们为MSN中的整体催化反应扩散过程应用了空间粗粒度（CG）随机模型。毛孔被视为细胞的线性阵列，从该物种的末端吸收和解吸，在物种之间跳跃和交换，交换速率反映了$\mathcal{P}$。CG模型预测（包括产量）通过动力学Monte Carlo模拟进行评估。